<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

                             ----------------------

                                    FORM 10-Q

(MARK ONE)

[x]         QUARTERLY REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
            EXCHANGE ACT OF 1934

For the quarterly period ended       March 31, 1998
                               -------------------------------

                                       OR

[ ]         TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
            EXCHANGE ACT OF 1934

For the transition period from _______________________ to ______________________

                         Commission File Number 0-13333
                                                -------

Enstar Income Program 1984-1, L.P.
--------------------------------------------------------------------------------
             (Exact name of Registrant as specified in its charter)

           Georgia                                             58-1581136
-------------------------------                          -----------------------
(State or other jurisdiction of                             (I.R.S. Employer
 incorporation or organization)                          Identification Number)

 10900 Wilshire Boulevard - 15th Floor
        Los Angeles, California                                  90024
----------------------------------------                 -----------------------
(Address of principal executive offices)                       (Zip Code)

Registrant's telephone number, including area code:   (310) 824-9990
                                                   --------------------


--------------------------------------------------------------------------------
               Former name, former address and former fiscal year,
                          if changed since last report.


            Indicate by check mark whether the registrant (1) has filed all
reports required to be filed by Section 13 or 15(d) of the Securities Exchange
Act of 1934 during the preceding 12 months (or for such shorter period that the
registrant was required to file such reports), and (2) has been subject to such
filing requirements for the past 90 days. Yes  X  No
                                             -----   -----


                        Exhibit Index located at Page E-1

<PAGE>   2

                         PART I - FINANCIAL INFORMATION

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                            CONDENSED BALANCE SHEETS

                       ==================================



<TABLE>
<CAPTION>
                                                                         December 31,        March 31,
                                                                            1997*              1998
                                                                         ------------       -----------
                                                                                            (Unaudited)
<S>                                                                      <C>                <C>
ASSETS:
   Cash and cash equivalents                                             $   462,900        $   570,700

   Accounts receivable, less allowance of $28,000 and
      $15,900 for possible losses                                            107,500             41,000

   Insurance claim receivable                                                399,700            392,400

   Prepaid expenses and other assets                                         135,800            169,200

   Property, plant and equipment, less accumulated
      depreciation and amortization of $10,477,900 and $10,596,800         3,387,200          3,570,700

   Franchise cost, net of accumulated
      amortization of $235,400 and $241,000                                   74,600             70,500

   Deferred loan costs and other charges, net                                128,400            118,800
                                                                         -----------        -----------

                                                                         $ 4,696,100        $ 4,933,300
                                                                         ===========        ===========

                                  LIABILITIES AND PARTNERSHIP CAPITAL
                                  -----------------------------------

LIABILITIES:
   Accounts payable                                                      $   529,800        $   476,100
   Due to affiliates                                                         754,200            745,000
   Note payable - affiliate                                                  250,000            250,000
                                                                         -----------        -----------

              TOTAL LIABILITIES                                            1,534,000          1,471,100
                                                                         -----------        -----------

COMMITMENTS AND CONTINGENCIES

PARTNERSHIP CAPITAL (DEFICIT):
   General partner                                                           (41,100)           (38,100)
   Limited partners                                                        3,203,200          3,500,300
                                                                         -----------        -----------

              TOTAL PARTNERSHIP CAPITAL                                    3,162,100          3,462,200
                                                                         -----------        -----------

                                                                         $ 4,696,100        $ 4,933,300
                                                                         ===========        ===========
</TABLE>



               *As presented in the audited financial statements.
            See accompanying notes to condensed financial statements.


                                       2

<PAGE>   3

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                       CONDENSED STATEMENTS OF OPERATIONS

                       ==================================


<TABLE>
<CAPTION>
                                                              Unaudited
                                                    -------------------------------
                                                          Three months ended
                                                               March 31,
                                                    -------------------------------
                                                       1997                 1998
                                                    -----------         -----------
<S>                                                 <C>                 <C>
REVENUES                                            $ 1,368,900         $ 1,330,000
                                                    -----------         -----------
OPERATING EXPENSES:
   Service costs                                        495,200             480,000
   General and administrative expenses                  197,300             180,900
   General Partner management fees
      and reimbursed expenses                           138,500             167,500
   Depreciation and amortization                        136,500             178,400
                                                    -----------         -----------

                                                        967,500           1,006,800
                                                    -----------         -----------

OPERATING INCOME                                        401,400             323,200
                                                    -----------         -----------

OTHER INCOME (EXPENSE):
   Interest income                                       11,600               4,500
   Interest expense                                     (29,000)            (27,600)
                                                    -----------         -----------

                                                        (17,400)            (23,100)
                                                    -----------         -----------

NET INCOME                                          $   384,000         $   300,100
                                                    ===========         ===========

Net income allocated to General Partner             $     3,800         $     3,000
                                                    ===========         ===========

Net income allocated to Limited Partners            $   380,200         $   297,100
                                                    ===========         ===========

NET INCOME PER UNIT OF LIMITED
   PARTNERSHIP INTEREST                             $     12.70         $      9.92
                                                    ===========         ===========

AVERAGE LIMITED PARTNERSHIP
   UNITS OUTSTANDING DURING PERIOD                       29,940              29,940
                                                    ===========         ===========
</TABLE>






            See accompanying notes to condensed financial statements.


                                        3

<PAGE>   4

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                            STATEMENTS OF CASH FLOWS

                       ==================================


<TABLE>
<CAPTION>
                                                                          Unaudited
                                                                 -----------------------------
                                                                      Three months ended
                                                                           March 31,
                                                                 -----------------------------
                                                                    1997              1998
                                                                 -----------       -----------
<S>                                                              <C>               <C>
CASH FLOWS FROM OPERATING ACTIVITIES:
   Net income                                                    $   384,000       $   300,100
   Adjustments to reconcile net income to net cash
      provided by operating activities:
         Depreciation and amortization                               136,500           178,400
         Amortization of deferred loan costs                           6,100             7,300
         Increase (decrease) from changes in:
            Receivables, prepaid expenses and other assets           (20,700)           40,400
            Accounts payable                                         (80,200)          (53,700)
                                                                 -----------       -----------

                 Net cash provided by operating activities           425,700           472,500
                                                                 -----------       -----------

CASH FLOWS FROM INVESTING ACTIVITIES:
   Capital expenditures                                             (122,600)         (352,200)
   Increase in intangible assets                                     (12,800)           (1,900)
                                                                 -----------       -----------

                 Net cash used in investing activities              (135,400)         (354,100)
                                                                 -----------       -----------

CASH FLOWS FROM FINANCING ACTIVITIES:
   Due to affiliates                                                 108,900            (9,200)
   Repayment of debt                                                (500,000)           --
   Deferred loan costs                                                --                (1,400)
                                                                 -----------       -----------

                 Net cash used in financing activities              (391,100)          (10,600)
                                                                 -----------       -----------

INCREASE (DECREASE) IN CASH AND
   CASH EQUIVALENTS                                                 (100,800)          107,800

CASH AND CASH EQUIVALENTS
   AT BEGINNING OF PERIOD                                          1,004,400           462,900
                                                                 -----------       -----------

CASH AND CASH EQUIVALENTS
   AT END OF PERIOD                                              $   903,600       $   570,700
                                                                 ===========       ===========
</TABLE>




            See accompanying notes to condensed financial statements.


                                       4
<PAGE>   5

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                     =======================================


1.          INTERIM FINANCIAL STATEMENTS

            The accompanying condensed interim financial statements for the
three months ended March 31, 1998 and 1997 are unaudited. These condensed
interim financial statements should be read in conjunction with the audited
financial statements and notes thereto included in the Partnership's latest
Annual Report on Form 10-K. In the opinion of management, such statements
reflect all adjustments (consisting only of normal recurring adjustments)
necessary for a fair presentation of the results of such periods. The results of
operations for the three months ended March 31, 1998 are not necessarily
indicative of results for the entire year.

2.          TRANSACTIONS WITH THE GENERAL PARTNER AND AFFILIATES

            The Partnership has a management and service agreement with a wholly
owned subsidiary of the General Partner (the "Manager") for a monthly management
fee of 5% of revenues, excluding revenues from the sale of cable television
systems or franchises. Management fee expense approximated $66,500 for the three
months ended March 31, 1998.

            In addition to the monthly management fee described above, the
Partnership reimburses the Manager for direct expenses incurred on behalf of the
Partnership and for the Partnership's allocable share of operational costs
associated with services provided by the Manager. All cable television
properties managed by the General Partner and its subsidiary are charged a
proportionate share of these expenses. The General Partner has contracted with
Falcon Holding Group, L.P. ("FHGLP"), an affiliated partnership, to provide
corporate management services for the Partnership. Corporate office allocations
and district office expenses are charged to the properties served based
primarily on the respective percentage of basic subscribers or homes passed
(dwelling units within a system) within the designated service areas. The total
amount charged to the Partnership for these services approximated $101,000 for
the three months ended March 31, 1998. Management fees and reimbursed expenses
due the General Partner are non-interest bearing.

            Payments of management fees and reimbursed expenses were deferred in
prior years pursuant to restrictions in the note payable agreement. The
cumulative amount deferred was approximately $1,081,300. On September 30, 1997,
the Partnership obtained new financing and subsequently used such borrowings and
other available cash to pay $619,000 of previously deferred management fees and
reimbursed expenses. The remainder of these deferred amounts, $462,300, was
contributed as an equity contribution by the General Partner to Enstar Finance
Company, LLC ("EFC"), a subsidiary of the General Partner, and remains an
outstanding obligation of the Partnership.

            The Partnership also receives certain system operating management
services from affiliates of the General Partner in addition to the Manager due
to the fact that there are no such employees directly employed by the
Partnership. The Partnership reimburses the affiliates for its allocable share
of the affiliates' operational costs. The total amount charged to the
Partnership for these costs approximated $8,300 in the three months ended March
31, 1998. No management fee is payable to the affiliates by the Partnership and
there is no duplication of reimbursed expenses and costs paid to the Manager.



                                       5
<PAGE>   6

                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                     NOTES TO CONDENSED FINANCIAL STATEMENTS

                     =======================================


2.          TRANSACTIONS WITH THE GENERAL PARTNER AND AFFILIATES (CONTINUED)

            Certain programming services have been purchased through an
affiliate of the Partnership. In turn, the affiliate charges the Partnership for
these costs based on an estimate of what the General Partner could negotiate for
such programming services for the 15 partnerships managed by the General Partner
as a group. The Partnership recorded programming fee expense of $291,300 for the
three months ended March 31, 1998. Programming fees are included in service
costs in the statements of operations.

3.          EARNINGS PER UNIT OF LIMITED PARTNERSHIP INTEREST

            Earnings and losses per unit of limited partnership interest is
based on the average number of units outstanding during the periods presented.
For this purpose, earnings and losses have been allocated 99% to the Limited
Partners and 1% to the General Partner. The General Partner does not own units
of partnership interest in the Partnership, but rather holds a participation
interest in the income, losses and distributions of the Partnership.

4.          RECLASSIFICATIONS

            Certain 1997 amounts have been reclassified to conform to the 1998
presentation.







                                       6

<PAGE>   7

                       ENSTAR INCOME PROGRAM 1984-1, L.P.


ITEM 2.      MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
             RESULTS OF OPERATIONS

INTRODUCTION

            The Cable Television Consumer Protection and Competition Act of 1992
(the "1992 Cable Act") required the Federal Communications Commission ("FCC")
to, among other things, implement extensive regulation of the rates charged by
cable television systems for basic and programming service tiers, installation,
and customer premises equipment leasing. Compliance with those rate regulations
has had a negative impact on the Partnership's revenues and cash flow. The
Telecommunications Act of 1996 (the "1996 Telecom Act") substantially changed
the competitive and regulatory environment for cable television and
telecommunications service providers. Among other changes, the 1996 Telecom Act
provides that the regulation of cable programming service tier ("CPST") rates
will be terminated on March 31, 1999. Because cable service rate increases have
continued to outpace inflation under the FCC's existing regulations, the
Partnership expects Congress and the FCC to explore additional methods of
regulating cable service rate increases, including deferral or repeal of the
March 31, 1999 termination of CPST rate regulation. There can be no assurance as
to what, if any, further action may be taken by the FCC, Congress or any other
regulatory authority or court, or the effect thereof on the Partnership's
business. Accordingly, the Partnership's historical financial results as
described below are not necessarily indicative of future performance.

            This Report includes certain forward looking statements regarding,
among other things, future results of operations, regulatory requirements,
competition, capital needs and general business conditions applicable to the
Partnership. Such forward looking statements involve risks and uncertainties
including, without limitation, the uncertainty of legislative and regulatory
changes and the rapid developments in the competitive environment facing cable
television operators such as the Partnership. In addition to the information
provided herein, reference is made to the Partnership's Annual Report on Form
10-K for the year ended December 31, 1997 for additional information regarding
such matters and the effect thereof on the Partnership's business.

RESULTS OF OPERATIONS

            The Partnership's revenues decreased from $1,368,900 to $1,330,000,
or by 2.8%, for the three months ended March 31, 1998 as compared to the
corresponding period in 1997. Of the $38,900 decrease, $84,300 was due to
decreases in the number of subscriptions for basic, premium, tier and equipment
rental services. The decrease was partially offset by a $35,600 increase due to
increases in regulated service rates that were implemented by the Partnership in
1997 and a $9,800 increase in other revenue producing items. As of March 31,
1998, the Partnership had approximately 11,100 basic subscribers and 4,700
premium service units.

            Service costs decreased from $495,200 to $ 480,000, or by 3.1%, for
the three months ended March 31, 1998 as compared to the corresponding period in
1997. Service costs represent costs directly attributable to providing cable
services to customers. The decrease was principally due to lower copyright fees,
personnel costs, franchise fees and programming expense. Copyright and franchise
fees decreased due to decreases in revenues as described above. The decrease in
franchise fees also resulted from a non-recurring charge in the first quarter of
1997 related to 1996 franchise fee payments made during the quarter which
exceeded



                                       7

<PAGE>   8

                       ENSTAR INCOME PROGRAM 1984-1, L.P.


RESULTS OF OPERATIONS (CONTINUED)

estimates recorded as of December 31, 1996. Personnel costs decreased due to
staff reductions. Programming expense decreased as a result of decreases in the
number of subscribers to certain premium channels.

            General and administrative expenses decreased from $197,300 to
$180,900 or by 8.3%, for the three months ended March 31, 1998 as compared to
the corresponding period in 1997. The decrease was primarily due to decreases in
personnel costs and expenses allocated by an affiliate of the General Partner
that discontinued management of the Partnership's Tennessee operations in the
fourth quarter of 1997. Such services are now being provided by the General
Partner.

            Management fees and reimbursed expenses increased from $138,500 to
$167,500, or by 20.9%, for the quarter ended March 31, 1998 as compared to the
corresponding period in 1997. Management fees decreased in direct relation to
decreased revenues as described above. Reimbursed expenses allocated by the
General Partner increased after system operating management of the Partnership's
Tennessee systems transferred from an affiliate to the General Partner.

            Operating income before income taxes, depreciation and amortization
(EBITDA) is a commonly used financial analysis tool for measuring and comparing
cable television companies in several areas, such as liquidity, operating
performance and leverage. EBITDA as a percentage of revenues decreased from
39.3% to 37.7% during the three months ended March 31, 1998 as compared to the
corresponding period in 1997. The decrease was primarily due to decreases in
revenues and increases in reimbursed expenses as described above. EBITDA
decreased from $537,900 to $501,600 or by 6.7%, during the three months ended
March 31, 1998 as compared to the corresponding period in 1997. EBITDA should be
considered in addition to and not as a substitute for net income and cash flows
determined in accordance with generally accepted accounting principles as an
indicator of financial performance and liquidity.

            Depreciation and amortization expense increased from $136,500 to
$178,400, or by 30.7%, for the quarter ended March 31, 1998 as compared to the
corresponding period in 1997. The increase was primarily due to asset additions
including expenditures in 1997 to replace segments of the Partnership's North
Carolina cable plant and subscriber connections that were damaged by a storm in
1996.

            Operating income decreased from $401,400 to $323,200, or by 19.5%,
for the three months ended March 31, 1998 as compared to the corresponding
period in 1997, primarily due to a decrease in revenues and increases in
depreciation and amortization expense and reimbursed expenses as described
above.

         Interest income decreased from $11,600 to $4,500, or by 61.2%, for the
three months ended March 31, 1998 as compared to the corresponding period in
1997. The decrease for the quarter was due to lower cash balances available for
investment.

         Interest expense decreased from $29,000 to $27,600, or by 4.8%, for the
three months ended March 31, 1998 as compared to the corresponding period in
1997, due to lower average borrowings in the 1998 quarter.




                                       8

<PAGE>   9

                       ENSTAR INCOME PROGRAM 1984-1, L.P.


RESULTS OF OPERATIONS (CONTINUED)

            Due to the factors described above, the Partnership's net income
decreased from $384,000 to $300,100, or by 21.8%, for the three months ended
March 31, 1998 as compared to the corresponding period in 1997.

LIQUIDITY AND CAPITAL RESOURCES

            The Partnership's primary objective, having invested its net
offering proceeds in cable systems, is to distribute to its partners all
available cash flow from operations and proceeds from the sale of cable systems,
if any, after providing for expenses, debt service and capital requirements. In
general, these requirements involve expansion, improvement and upgrade of the
Partnership's existing cable systems and were $352,200 in the first quarter of
1998. As of the date of this Report, substantially all of the available channel
capacity in the Partnership's systems is being utilized and each of such systems
requires an upgrade. The entire upgrade program is presently estimated to
require aggregate capital expenditures of approximately $8,000,000 and covers 12
franchise areas. These upgrades are currently required in two existing franchise
agreements. The cost to upgrade the two franchise areas is estimated to be
$2,336,000 and must be completed by December 2001 and February 2002,
respectively.

            On September 30, 1997, the Partnership entered into a loan agreement
with EFC for a revolving loan facility of $7,481,700 (the "Facility") of which
$250,000 was advanced to the Partnership at closing. The Partnership's
management expects to increase borrowings under the Facility for the upgrade of
the Partnership's systems.

            The Partnership's Facility will mature on August 31, 2001, at which
time all funds previously advanced will be due in full. Borrowings bear interest
at the lender's base rate (8.5% at March 31, 1998) plus 0.625%, or at an
offshore rate plus 1.875%. The Partnership is permitted to prepay amounts
outstanding under the Facility at any time without penalty, and is able to
reborrow throughout the term of the Facility up to the maximum commitment then
available so long as no event of default exists. If the Partnership has excess
cash flow and its ratio of debt to cash flow exceeds 4.25 to 1, or it receives
proceeds from sales of its assets in excess of a specified amount, the
Partnership is required to make mandatory prepayments under the Facility. Such
prepayments permanently reduce the maximum commitment under the Facility.

            The Facility contains certain financial tests and other covenants
including, among others, restrictions on incurrence of indebtedness,
investments, sales of assets, acquisitions and other covenants, defaults and
conditions. The Partnership believes it was in compliance with the covenants at
March 31, 1998.

            The Facility does not restrict the payment of distributions to
partners unless an event of default exists thereunder or the ratio of debt to
cash flow is greater than 4 to 1. However, due to the upgrade program discussed
above, the General Partner believes it is critical to conserve cash and
borrowing capacity and, consequently, has concluded that it is not prudent for
the Partnership to resume paying distributions at this time.

            As disclosed in previous filings, the General Partner may seek a
buyer for the Snow Hill, North Carolina system as well as for the Kershaw, South
Carolina system; however, the General Partner is not actively seeking buyers at
this time. The sale of these systems would allow the Partnership to reduce its
debt



                                       9

<PAGE>   10

                       ENSTAR INCOME PROGRAM 1984-1, L.P.


LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

or accelerate the rebuilding of its remaining systems. The Partnership is under
no obligation to sell these systems. Upon the sale of either or both of these
systems, the General Partner would evaluate the feasibility at that time of
resuming the payment of distributions. There can be no assurance that these
systems can be sold at an acceptable price, if at all.

            Beginning in August 1997, the Partnership elected to self-insure its
cable distribution plant and subscriber connections against property damage as
well as possible business interruptions caused by such damage. The decision to
self-insure was made due to significant increases in the cost of insurance
coverage and decreases in the amount of insurance coverage available.

            While the Partnership has made the election to self-insure for these
risks based upon a comparison of historical damage sustained over the past five
years with the cost and amount of insurance currently available, there can be no
assurance that future self-insured losses will not exceed prior costs of
maintaining insurance for these risks. Approximately 65% of the Partnership's
subscribers are served by its system in Brownsville, Tennessee and neighboring
communities. Significant damage to the system due to seasonal weather conditions
or other events could have a material adverse effect on the Partnership's
liquidity and cash flows. The Partnership continues to purchase insurance
coverage in amounts its management views as appropriate for all other property,
liability, automobile, workers' compensation and other types of insurable risks.

            The "Year 2000" issue refers to certain contingencies that could
result from computer programs being written using two digits rather than four to
define the year. Many existing computer systems, including certain of the
Partnership's computer systems, process transactions based on two digits for the
year of the transaction (for example, "98" for 1998). These computer systems may
not operate effectively when the last two digits become "00," as will occur on
January 1, 2000.

            The General Partner has commenced an assessment of the Partnership's
Year 2000 business risks and its exposure to computer systems, to operating
equipment which is date sensitive and to the interface systems of its vendors
and service providers. Based on a preliminary study, the General Partner has
concluded that certain of the Partnership's information systems were not Year
2000 compliant and has elected to replace such software and hardware with Year
2000 compliant applications and equipment, although the decision to replace
major portions of such software and hardware had previously been made without
regard to the Year 2000 issue. The General Partner expects to install
substantially all of the new systems in 1998, with the remaining systems to be
installed in the first half of 1999. The total anticipated cost, including
replacement software and hardware, will be borne by FHGLP.

            In addition to evaluating internal systems, the General Partner has
also initiated communications with third party vendors and service suppliers to
determine the extent to which the Partnership's interface systems are vulnerable
should those third parties fail to solve their own Year 2000 problems on a
timely basis. There can be no assurance that the systems of other companies on
which the Partnership's systems rely will be timely converted and that the
failure to do so would not have an adverse impact on the Partnership's systems.
The General Partner continues to closely monitor Year 2000 developments with
vendors and service suppliers.



                                       10

<PAGE>   11

                       ENSTAR INCOME PROGRAM 1984-1, L.P.


LIQUIDITY AND CAPITAL RESOURCES (CONTINUED)

            THREE MONTHS ENDED MARCH 31, 1998 AND 1997

            Operating activities provided $46,800 more cash in the three months
ended March 31, 1998 than in the corresponding period in 1997. Changes in
accounts receivable, prepaid expenses and other assets provided $61,100 more
cash in the first three months of 1998 due to differences in the timing of
receivable collections and in the payment of prepaid expenses. The Partnership
used $26,500 less cash for accounts payable due to differences in the timing of
payments.

            The Partnership used $218,700 more cash in investing activities in
the three months ended March 31, 1998 than in the corresponding three months of
1997 due to a $229,600 increase in expenditures for tangible assets, partially
offset by a $10,900 decrease in expenditures for intangible assets.

            Financing activities used $380,500 less cash in the first three
months of 1998 than in the comparable 1997 period. The Partnership used $500,000
less cash for the repayment of debt, partially offset by an increase of $118,100
for the payment of amounts owed to the General Partner and other affiliates.

INFLATION

            Certain of the Partnership's expenses, such as those for wages and
benefits, equipment repair and replacement, and billing and marketing generally
increase with inflation. However, the Partnership does not believe that its
financial results have been, or will be, adversely affected by inflation in a
material way, provided that the Partnership is able to increase its service
rates periodically, of which there can be no assurance.





                                       11

<PAGE>   12

                       ENSTAR INCOME PROGRAM 1984-1, L.P.


PART II.          OTHER INFORMATION


ITEMS 1-5.        Not applicable.

ITEM 6.           Exhibits and Reports on Form 8-K

                  (a)      Exhibit 10.27 - Franchise Ordinance thereto granting
                           a non-exclusive community antenna television
                           franchise for Greene County, North Carolina.

                  (b)      No reports on Form 8-K were filed during the quarter
                           for which this report is filed.




<PAGE>   13

                                   SIGNATURES


Pursuant to the requirements of the Securities Exchange Act of 1934, the
Registrant has duly caused this report to be signed on its behalf by the
undersigned thereunto duly authorized.



                       ENSTAR INCOME PROGRAM 1984-1, L.P.

                          a GEORGIA LIMITED PARTNERSHIP
                          -----------------------------
                                  (Registrant)



                                      By: ENSTAR COMMUNICATIONS CORPORATION
                                          General Partner






Date:  May 14, 1998                   By: /s/ Michael K. Menerey
                                          --------------------------------
                                          Michael K. Menerey,
                                          Executive Vice President,
                                          Chief Financial Officer and
                                          Secretary


<PAGE>   14


                       ENSTAR INCOME PROGRAM 1984-1, L.P.



                                  EXHIBIT INDEX


Exhibit
Number                             Description

10.27          Franchise Ordinance thereto granting a non-exclusive community
               antenna television franchise for Greene County, North Carolina.











                                      E-1